December 7, 2010
J.M.H
===Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question: How are rates, ratios and proportions related and how are they different?
Steps for the experiment:===
- Remove exactly 100 beans from a container of beans, and mark them with a pen or marker.
- Put the marked beans back into the container, and shake or mix them with the unmarked beans.
- Without lokking at the beans, scoop out a handful of about 30 beans. Record the numbers of marked and unmarked beans in this
sample. Return the sample to the jar, and mix the beans together again.
- Repeat this scoop-and-count procedure four more times. In each case, record the number of marked and unmarked beans.
Random data of the experiment:
Scoops
Marked Beans
Unmarked Beans
Total Captured
1
6
24
30
2
3
17
20
3
5
18
23
4
7
24
31
5
8
19
27
Problem 5.2 A. Study the data you collected. Use this data to estimate the number of beans in your container. Explain how you made your estimate.
From my data, I estimated that there are 481 beans in the container. I estimated this by first making ratios of beans marked over beans captured. Then I put them in proportions with the number 100 on top of the second fraction bar because there were 100 marked beans in the whole container.
For example: Scoop 1: 6marked/30captured = 100marked/500captured(total population)
I did this with the rest of the scoops, and then took the average of all the total population numbers which resulted into 481.42, which I rounded off to 481 beans.
B. Based on what you have learned from this experiment, how do you think biologists count deer populations?
Based on the experiment, biologists probably count deer populations by the capture-tag-recapture with beans method but with more tries to find the right average.
Problem 5.2 Follow-Up In your group, discuss ways in which this method might give a poor estimate of the actual number of deer in a population. Record your ideas.
Ways this experiment might give a poor estimate of the actual deer population are having the wrong size of the bean container, not being able to mark the beans or not being able to count marked over unmarked properly because of the size of the beans.
J.M.H
===Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
Essential Question:
How are rates, ratios and proportions related and how are they different?
Steps for the experiment:===
- Remove exactly 100 beans from a container of beans, and mark them with a pen or marker.
- Put the marked beans back into the container, and shake or mix them with the unmarked beans.- Without lokking at the beans, scoop out a handful of about 30 beans. Record the numbers of marked and unmarked beans in this
sample. Return the sample to the jar, and mix the beans together again.
- Repeat this scoop-and-count procedure four more times. In each case, record the number of marked and unmarked beans.
Random data of the experiment:
Scoops
Marked Beans
Unmarked Beans
Total Captured
A. Study the data you collected. Use this data to estimate the number of beans in your container. Explain how you made your estimate.
From my data, I estimated that there are 481 beans in the container. I estimated this by first making ratios of beans marked over beans captured. Then I put them in proportions with the number 100 on top of the second fraction bar because there were 100 marked beans in the whole container.
For example: Scoop 1: 6marked/30captured = 100marked/500captured(total population)
I did this with the rest of the scoops, and then took the average of all the total population numbers which resulted into 481.42, which I rounded off to 481 beans.
B. Based on what you have learned from this experiment, how do you think biologists count deer populations?
Based on the experiment, biologists probably count deer populations by the capture-tag-recapture with beans method but with more tries to find the right average.
Problem 5.2 Follow-Up
In your group, discuss ways in which this method might give a poor estimate of the actual number of deer in a population. Record your ideas.
Ways this experiment might give a poor estimate of the actual deer population are having the wrong size of the bean container, not being able to mark the beans or not being able to count marked over unmarked properly because of the size of the beans.